Permutations and Combinations

Permutations and Combinations Education

In mathematics, permutations and combinations are two different words that are used to express a group that includes an object by choosing or selecting them in a formation of subsets or sets. The different ways of arranging certain data in a group define the permutations and combinations. The selection of objects or data is defined as the permutations whereas the order in which they are expressed is regarded as the combinations. These two words play a very significant role in mathematics. In this article, we will try to cover some basic concepts such as differences between them, real-life examples of permutations and combinations and uses of them and do a detailed analysis about them. 

Differences Between Permutations and Combinations

In the paragraph mentioned above, we dealt with the definitions of permutation and combinations. In this passage, we will try to cover some major differences between permutations and combinations. The following points analyzes the distinguishing features of permutations and combinations.

  1. The selection of objects or data is defined as the permutations whereas the order in which they are expressed is regarded as the combinations. Whenever the arrangement is required the formula for permutation comes into work, but in combinations, the sequence of the arrangements is not required. 
  2. You may observe that, when objects of a similar kind are present, the use of combination prevails whereas, when objects of different kinds are present, the use of permutation prevails. 
  3. Whenever you calculate a question for permutations and combinations, the answer of permutation is always larger than the answer of combinations for the set of r and n values. 
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Some Real-life Examples of Permutations and Combinations


  • The arrangement of letters, colors, digits, people, numbers, etc are examples of permutation.
  • The procedure of choosing a pitcher or a captain or a shortstop from a team/group is known as permutation.
  • The arrangement of the first, second, and third places for the winners is also done with the help of a permutation formula.
  • You may have chosen a favorite color of yours in an order from a brochure of color, but did you know that this arrangement also comes under permutations. 


  • The selection of food, subjects, teams, and clothes is an arrangement done with the help of a combination formula.
  • The procedure of choosing three teams particularly from a group is known as combinations. 
  • Choosing three winners of no specific position is also an example of a combination. 
  • The process of picking or choosing any two colors of no specific designation from a brochure of color is also an example of a combination.

If you want to learn about permutations and combinations in a detailed manner, in a fun way, and in an interactive manner, you may visit Cuemath’s website.

Learn Math from Cuemath Website

Mathematics is a significant subject for children because it teaches them what numbers are and how they relate to real-life situations. For example, if you go to a market to buy some goods and you do not know how to operate some basic arithmetic operations such as addition or multiplication, you will be in a troublesome situation. Thus, math becomes a very important subject, but it won’t help you until the concept is grasped completely. When dealing with topics such as permutation and combination, students might feel tough to grasp the concept. That is when the job of Cuemath comes into play. It not only provides you with one-to-one sessions but also with various puzzles and worksheets. If you find the topic of permutation and combination very difficult to understand visit the Cuemath website to learn math and understand the concept in a fun and easy way.

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